H$$_{\infty }$$ controller for the vibration suppression of rolling mill systems with time-varying input delay

Abstract

The rolling mill system has the characteristic of measurement delay. In order to deal with the effects of time-delayed feedback from strip thickness measurement on vibration suppression, this paper studies the vibration suppression control strategy for the rolling mill system under time varying delay. Initially, the nonlinear rolling force and disturbance are taken into consideration during the dynamic rolling process. The mechanism-hydraulic coupling vibration model is established based on the flow equation and Newton's second law. Meanwhile, input delay caused by strip thickness measurement is considered in the rolling mill system and a time-delayed coupling vibration statespace model is introduced via choosing the appropriate state variables. Secondly, the corresponding linear matrix inequalities (LMIs) are derived from an augmented Lyapunov-Krasovskii functional (LKF) with advanced inequalities and are used to synthesize a controller that can achieve the asymptotical stability and H ∞ performance index. Finally, the effectiveness of the proposed control algorithm is verified by simulation experiment results.